Fast and Robust Algorithm for the Energy Minimization of Spin Systems Applied in an Analysis of High Temperature Spin Configurations in Terms of Skyrmion Density

An algorithm for the minimization of the energy of magnetic systems is presented and applied to the analysis of thermal configurations of a ferromagnet to identify inherent structures, i.e. the nearest local energy minima, as a function of temperature. Over a rather narrow temperature interval, skyrmions appear and reach a high temperature limit for the skyrmion density. In addition, the performance of the algorithm is further demonstrated in a self-consistent field calculation of a skyrmion in an itinerant magnet. The algorithm is based on a geometric approach in which the curvature of the spherical domain is taken into account and as a result the length of the magnetic moments is preserved in every iteration. In the limit of infinitesimal rotations, the minimization path coincides with that obtained using damped spin dynamics while the use of limited-memory quasi-newton minimization algorithms, such as the limited-memory Broyden-Fletcher-Goldfarb-Shanno (LBFGS) algorithm, significantly accelerates the convergence

Variational density functional calculations of excited states via direct optimization

The development of variational density functional theory approaches to excited electronic states is impeded by limitations of the commonly used self-consistent field (SCF) procedure. A method based on a direct optimization approach as well as the maximum overlap method is presented and the performance compared with previously proposed SCF strategies. Excited-state solutions correspond to saddle points of the energy as a function of the electronic degrees of freedom. The approach presented here makes use of a preconditioner determined with the help of the maximum overlap method to guide the convergence on a target nth-order saddle point. The method is found to be more robust and to converge faster than previously proposed SCF approaches for a set of 89 excited states of molecules. A limited-memory formulation of the symmetric rank-one method for updating the inverse Hessian is found to give the best performance. A conical intersection for the carbon monoxide molecule is calculated without resorting to fractional occupation numbers. Calculations on excited states of the hydrogen atom and a doubly excited state of the dihydrogen molecule using a self-interaction corrected functional are presented. For these systems, the self-interaction correction is found to improve the accuracy of density functional calculations of excited states

Os programas de transferência de renda condicionada: análise nos municípios de Santa Catarina de 2004 a 2008

TCC (graduação) - Universidade Federal de Santa Catarina, Centro Sócio Econômico, Curso de Ciências Econômicas.Criados pelo Governo Federal com o objetivo de reduzir a pobreza e melhorar a distribuição de renda no país, os programas de transferência de renda condicionada também foram de fundamental importância para que o Brasil atingisse o desenvolvimento obtido nos últimos anos. De acordo com dados do IPEA, esses programas, além de ter caráter social, gerar demanda por serviços básicos e melhorar a distribuição de renda da população, aumentam o consumo e a renda das pessoas, o que motiva um efeito multiplicador no mercado interno. O principal programa dessa natureza no país é o Programa Bolsa Família, que atende 13 milhões de famílias e cerca de 50 milhões de pessoas. O presente trabalho faz um estudo da atuação do Programa Bolsa Família no Brasil e em Santa Catarina e, mediante aplicação do critério de Calinski e Harabasz e da análise de cluster, identifica, nos municípios catarinenses nos anos de 2004, 2006 e 2008, características do PIB per capita e relação da quantidade de famílias beneficiadas pelo PBF e estimativa da população. Por fim, a análise de cluster confirma a existência de heterogeneidade dos municípios catarinenses nas três variáveis aplicadas. Conclui-se que o PBF contribui de forma significativa para o alívio da pobreza e redução da desigualdade de renda, mas existe um potencial de crescimento e distribuição a ser alcançado para que o programa consiga se consolidar e possibilitar uma melhor evolução do desenvolvimento dos municípios de Santa Catarina

Direct Optimization Method for Variational Excited-State Density Functional Calculations Using Real Space Grid or Plane Waves

A direct optimization method is presented for density functional calculations of excited electronic states using either a real space grid or a plane wave basis set. The method is variational, provides atomic forces in the excited states, and can be applied to Kohn-Sham (KS) functionals as well as orbital-density dependent functionals (ODD) including explicit self-interaction correction. The implementation for KS functionals involves two nested loops: (1) An inner loop for finding a stationary point in a subspace spanned by the occupied and a few virtual orbitals corresponding to the excited state; (2) an outer loop for minimizing the energy in a tangential direction. For ODD functionals, a third loop is used to find the unitary transformation that minimizes the energy functional among occupied orbitals only. Combined with the maximum overlap method, the algorithm converges in challenging cases where conventional self-consistent field algorithms tend to fail. The benchmark tests presented include two charge-transfer excitations in nitrobenzene and an excitation of CO to degenerate $\pi^\ast$ orbitals where the importance of complex orbitals is illustrated. An application of the method to several metal-to-ligand charge-transfer and metal-centred excited states of an Fe$^{\rm II}$ photosensitizer complex is described and the results compared to reported experimental estimates. The method is also used to study the effect of Perdew-Zunger self-interaction correction on valence and Rydberg excited states of several molecules, both singlet and triplet states. The correction is found to improve the description of molecular bond stretching but calculated values of the excitation energy are improved only slightly, by {\it ca.} 0.1 eV, due to cancellation of the estimated self-interaction error in the ground and excited states.Comment: 55 pages, 12 figures, including supporting Informatio

Direct Energy Minimization Based on Exponential Transformation in Density Functional Calculations of Finite and Extended Systems

The energy minimization involved in density functional calculations of electronic systems can be carried out using an exponential transformation that preserves the orthonormality of the orbitals. The energy of the system is then represented as a function of the elements of a skew-Hermitian matrix that can be optimized directly using unconstrained minimization methods. An implementation based on the limited memory Broyden-Fletcher-Goldfarb-Shanno approach with inexact line search and a preconditioner is presented and the performance compared with that of the commonly used self-consistent field approach. Results are presented for the G2 set of 148 molecules, liquid water configurations with up to 576 molecules and some insulating crystals. A general preconditioner is presented that is applicable to systems with fractional orbital occupation as is, for example, needed in the k-point sampling for periodic systems. This exponential transformation direct minimization approach is found to outperform the standard implementation of the self-consistent field approach in that all the calculations converge with the same set of parameter values and it requires less computational effort on average. The formulation of the exponential transformation and the gradients of the energy presented here are quite general and can be applied to energy functionals that are not unitary invariant such as self-interaction corrected functionals

Variational calculations of excited states via direct optimization of the orbitals in DFT

Post-print (lokagerð höfundar)A direct optimization method for obtaining excited electronic states using density functionals is presented. It involves selective convergence on saddle points on the energy surface representing the variation of the energy as a function of the electronic degrees of freedom, thereby avoiding convergence to a minimum and corresponding variational collapse to the ground electronic state. The method is based on an exponential transformation of the molecular orbitals, making it possible to use efficient quasi-Newton optimization approaches. Direct convergence on a target nth-order saddle point is guided by an appropriate preconditioner for the optimization as well as the maximum overlap method. Results of benchmark calculations of 52 excited states of molecules indicate that the method is more robust than a standard self-consistent field (SCF) approach especially when degenerate or quasi-degenerate orbitals are involved. The method can overcome challenges arising from rearrangement of closely spaced orbitals in a charge-transfer excitation of the nitrobenzene molecule, a case where the SCF fails to converge. The formulation of the method is general and can be applied to non-unitary invariant functionals, such as self-interaction corrected functionals.The present work was funded by the Icelandic Research Fund (grant number 196070-052) and the University of Iceland Research Fund. AVI is supported by a doctoral fellowship from the University of Iceland.Peer Reviewe

Hydrogeoecological estimation of the fresh waters state of the Nadym-Pursk and Pur-Taz oil and gas provinces of the Yamal-Nenets Autonomous District in connection with intensive mining of hydrocarbon deposits

In recent years the problem of rational use and protection of the country’s groundwater resources has become increasingly important. This is due to want of reserves of groundwater and surface water, their depletion with technological progress and the ever increasing influence of human economic activity. The growth of cities, industry, expansion of water consumption for various economic needs significantly change the water balance regimes on the surface, in soils and rocks.The northern part of the West Siberian Artesian Megabasin (WSAMB) is located on the territory of the Yamal-Nenets Autonomous District (YNAD). Now the district is an intensively developing region of the Russian Federation. Here, oil and gas are extracted, large transport communications and residential areas are located. The district is characterized by extreme landscape, climatic and geoecological conditions that determine the nature of development of dangerous natural processes, the interaction of surface and groundwater and the migration of pollutants. The anthropogenic impact on the fresh groundwater of WSAMB and the increase in the residential load in the developed territories, which is intensified as a result of oil and gas production, requires an in-depth study of the regional hydrodynamics of the Upper Eocene Quaternary hydro-geological complex.The article provides calculations of mass flows of the main pollutants in groundwater and provides a preliminary forecast of the possible change in the quality of fresh water under the influence of anthropogenic factor